Fields and matrices

Fields are global variables provided by Taichi. Fields can be either sparse or dense. An element of a field can be either a scalar or a vector/matrix.


Matrices can be used as field elements, so you can have fields with each element being a matrix.

Scalar fields

  • Every global variable is an N-dimensional field.

    • Global scalars are treated as 0-D scalar fields.
  • Fields are always accessed using indices

    • E.g. x[i, j, k] if x is a 3D scalar field.
    • Even when accessing 0-D field x, use x[None] = 0 instead of x = 0. Please always use indexing to access entries in fields.
  • Field values are initially zero.

  • Sparse fields are initially inactive.

  • See Scalar fields for more details.

Matrix fields

Field elements can also be matrices.

Suppose you have a 128 x 64 field called A, each element containing a 3 x 2 matrix. To allocate a 128 x 64 matrix field which has a 3 x 2 matrix for each of its entry, use the statement A = ti.Matrix.field(3, 2, dtype=ti.f32, shape=(128, 64)).

  • If you want to get the matrix of grid node i, j, please use mat = A[i, j]. mat is simply a 3 x 2 matrix
  • To get the element on the first row and second column of that matrix, use mat[0, 1] or A[i, j][0, 1].
  • As you may have noticed, there are two indexing operators [] when you load an matrix element from a global matrix field: the first is for field indexing, the second for matrix indexing.
  • ti.Vector is simply an alias of ti.Matrix.
  • See Matrices for more on matrices.

Matrix size

For performance reasons matrix operations will be unrolled, therefore we suggest using only small matrices. For example, 2x1, 3x3, 4x4 matrices are fine, yet 32x6 is probably too big as a matrix size.


Due to the unrolling mechanisms, operating on large matrices (e.g. 32x128) can lead to very long compilation time and low performance.

If you have a dimension that is too large (e.g. 64), it’s better to declare a field of size 64. E.g., instead of declaring ti.Matrix.field(64, 32, dtype=ti.f32, shape=(3, 2)), declare ti.Matrix.field(3, 2, dtype=ti.f32, shape=(64, 32)). Try to put large dimensions to fields instead of matrices.